Mechanism research of temperature and discharge rate effects on sodium-ion battery capacity degradation

In this paper, a robustness evaluation of Unscented Kalman Filter (UKF) in comparison with the Extended Kalman Filter (EKF) for State of Charge (SOC) estimation of a lithium-ion battery based on capacity degradation model is investigated. To more comprehensively evaluate the performance of EKF and UKF, A first-order RC equivalent circuit model was used to characterize the dynamic behavior of a 30Ah lithium-ion battery. Based on the relationship between the Arrhenius formula, battery capacity, temperature and charge-discharge current accelerated stress, a fitting formula is obtained to predict the battery capacity degradation rate. The simulation results show that UKF outperforms EKF in terms of estimation accuracy and convergence rate against temperature effects, current and voltage noises.

Failure in battery could lead in loss of operation, decreased capability, operational impairment and downtime. If capacity degradation in battery can be predicted, terrible failure can be avoided. This paper presents developed grey prediction algorithm for predicting battery's capacity degradation. Basic grey model have employed to forecast degradation of battery's capacity, but the result was unsatisfactory. In order to improve the accuracy of prediction, the basic grey model has been modified. The proposed method is validated by predicting capacity degradation of a tested battery. This work also achieved that grey model is a promising predictor for battery prognostics system.

Problem. The article is devoted to the problem of increasing the safety, environmental friendliness and efficiency of vehicles through the use of lithium-ion batteries, predicting their final service life using a new predictive model of capacity degradation. The analysis of the performance and degradation of lithium-ion batteries is carried out and the factors of their degradation are studied. A predictive model of the degradation of the capacity of lithium-ion batteries in electric vehicles has been developed, which determines the remaining useful life of the battery and predicts its life cycle using data only from early charge/discharge cycles, during which significantly less degradation occurs. Methods for increasing the service life of electric vehicle batteries are given. Goal. The aim of the work is to improve the safety, environmental friendliness and efficiency of electric vehicles by determining the predicted final resource of lithium-ion batteries using a new predictive model of capacity degradation. Methodology. Methods of scientific analysis and synthesis of increasing the service life of batteries. A predictive model of capacity degradation of lithium-ion batteries of electric vehicles determines the remaining useful life of the battery and predicts its life cycle. The results. Based on the analysis of publications and studies, a predictive model of capacity degradation of lithium-ion batteries was developed. As a result, the final resource of lithium-ion batteries is predicted. An important aspect of the concept of predicting the state of degradation of the battery capacity is that the data analysis in combination with the results of this study demonstrates a virtually linear relationship between the life cycle, inflection point and curvature point. Methods for increasing the service life of batteries of electric vehicles and prolonging their life cycle through the rational use of an electric vehicle are considered. The results of the research coincide with the developed predictive model of lithium-ion battery capacity degradation, which determines that at each charge/discharge cycle, the electric vehicle battery loses an average of 0.015 % of its capacity over the entire life cycle. The considered methods for increasing the battery life, which allows increasing the number of charge/discharge cycles and the life cycle due to the rational use of the electric vehicle. Originality. The peculiarity of the developed predictive model of lithium-ion battery capacity degradation in electric vehicles is that the battery life cycle is determined by using data from the first charge/discharge cycles (from 200 to 250), where minor degradation still occurs. But such data will be sufficient to identify the distortion point, then the inflection point and then determine the full service life of the electric vehicle battery, which is limited to 80% of the useful capacity. Practical value. A predictive model for the capacity degradation of lithium-ion batteries in electric vehicles determines the remaining useful life of the battery and predicts its service life, which is an important issue for both electric vehicle owners (both new and used) and electric vehicle manufacturers (for the formation of warranty obligations and battery operation strategies).

SUMMARY & CONCLUSIONSThis work introduces a systematic approach to model the degradation of the capacity of lithium-ion (li-ion) batteries in Electronic Heating Systems (EHS) products and relates the model to field capacity degradation based on the users’ usage pattern. The current literatures on battery capacity estimation focus on the mathematical evaluation based on electrochemical, semi-empirical, and data-driven models. However, these approaches lack the connection to predicting battery degradation based on actual usage pattern in the field.By utilizing the Accelerated Life Test (ALT) data and battery knowledge, the proposed methodology facilitates the integration of non-linear regression-based Transfer Function (TF) with Monte Carlo simulation for the prediction of the battery capacity degradation. This enables the battery system designers to make data-driven decisions.The method is applied to small hand-held li-ion battery-driven EHS products. Parameters affecting the battery capacity degradation of such devices include continuous usage with intermittent resting before charging, variable resting time, and different usage durations. The TF helps in relating these critical parameters to the battery capacity degradation. The outcome of the methodology is then compared with the actual field performance where a good approximation is observed.Historically, Philip Morris Products (PMP) SA used usage cycle and linear-regression model to predict battery capacity degradation based on the worst-case users. By implementing this non-linear modeling approach integrated with Monte Carlo methodology, it is possible to fit the field usage pattern (month-to-month) to precisely predict the device usage limitation constrained by battery degradation. This was combined with an extrapolation to predict a possible warranty extension.

Li-ion batteries (LiBs) are widely adopted in electric vehicles (EVs) owing to their superior properties, such as high energy density, low discharge rate, long lifespan, and lightweight construction. Since the battery pack is the sole energy source for an EV, its performance is critical for optimal vehicle operation. However, the battery's calendar life, cycle life, and overall performance are significantly affected by temperature variations. The Li-ion batteries used in EVs may encounter challenging working conditions, leading to thermal problems such as significant capacity and power loss. In contrast, thermal runaways can occur at temperatures above a specific threshold, leading to severe health deterioration and sometimes catastrophic safety hazards such as fires and explosions. As the temperature significantly impacts Li-ion batteries, a battery thermal management system that can efficiently dissipate heat is crucial to ensure the battery's optimal performance and longevity. Hence, it is crucial to develop accurate algorithms for battery thermal management systems to precisely and dynamically estimate the temperature dynamics of the batteries integrated within the battery pack.While experimental data can be used to estimate battery temperatures, the dynamic and diverse operating conditions of electric vehicles (EVs) present a significant challenge. Therefore, accurately predicting thermal response within batteries is critical. Various thermal models have been developed to predict the thermal behavior of batteries and quantify the amount of heat generated. The simplified thermal model only considers joule heating and reversible entropic heating. However, more accurate physics-based models consider reversible heat caused by the side reactions, heat generated by mass transport loss, and even mixing-induced heat. The amount of heat generated inside a Li-ion battery is determined by its equivalent internal resistance, open circuit voltage, and entropy change, which are in turn influenced by temperature and depth of discharge (DoD). To the best of the authors' knowledge, previous research on the heat generation of Li-ion batteries has been limited in some respects. Specifically, there has been little investigation into the combined impact of temperature and depth of discharge (DoD) across a wide temperature range. Most studies have been conducted under ambient temperature conditions, and only a few have focused on high temperatures within a narrow range with low discharge rates.Thus, this study aims to address the research gap regarding the impact of temperature and depth of discharge (DoD) on heat generation in Li-ion batteries by analyzing these parameters using a transient battery thermal model. The research intends to improve the accuracy and precision of battery thermal behavior prediction, which has broad implications for battery-powered applications. This study aims to evaluate the impact of different resistance models on heat generation in Li-ion batteries, explicitly comparing a constant resistance model with a model that considers resistance as a function of temperature and depth of discharge (DoD). Investigating the interdependent impact of battery temperature and DoD on heat generation is crucial to create an accurate battery thermal model with high fidelity. The current study uses a two-dimensional battery thermal model to comprehensively analyze thermal behavior of a LiFePO4-20Ah Li-ion pouch cell. In this research study, heat generation in a Li-ion battery is evaluated by estimating the internal resistance and entropic change obtained from experimentation. The energy equation is then solved using the finite difference method in MATLAB to obtain the transient thermal response of the battery. The developed transient electrothermal model is validated against experimental data under varying C rates to assess the accuracy and precision of the proposed model. The simulation results show that the thermal response obtained considering the effect of temperature and DoD on heat generation shows more accurate results than the constant resistance values. The thermal behavior of a LiFePO4 pouch cell, considering constant values for heat generation, has a maximum relative error of roughly 19.99% compared to experimental data at a 4C discharge rate. While this maximum relative error was reduced to 6.29% when considering the effect of temperature and DoD on heat generation. In the constant resistance model, more significant errors can be attributed to the fact that the resistance of a Li-ion battery varies with the depth of discharge (DoD). While the initial discharge phase of the battery exhibits minimal changes in resistance values, a substantial increase in resistance occurs during the final stages of discharge. This contrasts with the actual behavior of Li-ion batteries, which demonstrate significant variations in resistance values throughout the discharge process. Thus, coupling the effects of DoD and temperature on heat generation is necessary to accurately predict the thermal behavior of Li-ion battery. Figure 1

In this study, the dynamic model of a vanadium redox flow battery (VRFB) was developed to analyze the battery performance and capacity degradation caused by an electrolyte imbalance from hydrogen and oxygen evolution and self-discharge side reactions. The model-based analysis of the VRFB performance revealed that the rate of battery capacity loss resulting from the electrolyte imbalance considerably depended on electrode and membrane material as well as operating conditions. Self-discharge reactions were controlled by the operational time of the battery. In addition, the rate of capacity degradation increased with an increase in the total vanadium concentration and operating temperature, affecting the increased rates of the gassing and self-discharge side reactions. It was also found that operating the VRFB with variable flow rate did not improve the battery capacity and efficiency during long-term operation due to the electrolyte imbalance. To solve this problem, the dynamic optimization was performed to determine an optimal electrolyte flow rate. The obtained optimal flow rate profile can maximize the system efficiency, regarding the variation in an open circuit voltage and concentration overpotentials, and the electrolyte imbalance level. To further improve the performance of the VRFB, an on-line dynamic optimization was proposed for updating the optimal flow rate when the battery is operated under the intermittent current density. The extended Kalman filter was integrated into the proposed on-line optimization to estimate the current state of the vanadium concentration in the VRFB from the measurement of modified open circuit voltage. The results showed that the on-line optimization approach can increase the VRFB system efficiency and prevent the battery voltage from reaching to the limited voltage before the battery achieve the desired state of charge.

Adaptive state of charge estimation of Lithium-ion battery based on battery capacity degradation model

The capacity degradation characteristics of 18650 NCA lithium battery under different working conditions were investigated. Experiments were carried out at 45℃, and the direct effects of charge-discharge ratio and cut-off voltage on capacity degradation were analyzed. The results show that when the charge-discharge ratio is 2C, the capacity degradation rate is significantly higher than 1C and 1.5C. The degradation of battery capacity is more obvious in high cut-off voltage and high temperature environment. Through XRD and XPS characterization, it was found that high temperature resulted in the formation of lithium dendrites and the destruction of material structure, which affected the crystal state and chemical composition of the battery surface. The comprehensive analysis shows that the charge-discharge ratio and cut-off voltage are the key factors affecting the capacity degradation of 18650 NCA lithium battery. Optimizing these conditions can effectively delay the capacity decline and improve the service life and stability of the battery.

Owing to the fact that the existing battery capacity degradation detection method ignores the changes of battery internal morphological structure as the cycle number increases, it is hard to predict the rapid capacity degradation of the battery during the cycle process, which leads to errors of the battery capacity degradation detection result. This paper analyzes the changes in the morphological structure of the battery under different cycle numbers by means of tomographic images. At the same time, through the method of numerical analysis, the impact that the battery internal morphological structure change exerts on the battery capacity degradation is quantitatively analyzed, which provides a new way for detecting the capacity degradation of lithium ion battery.

There are two factors that affects battery capacity, ambient temperature and discharge rate. Ambient temperature can affect battery parameters such as voltage, capacity and battery life. Battery discharge current is influenced by the load associated with the battery. The load used needs to be adjusted to the battery capacity that will be used so that the discharge current produced by the battery is in accordance with its rating of use as the discharge flow generated by the battery can affect the battery’s capacity. Therefore, research on the effect of environmental temperature and current discharge on lead-acid batteries with a deep-discharge method is required to see the battery capacity at different ambient and discharge temperatures. From the research that have been carried out, the capacity ratio is directly proportional to the ambient temperature and inversely proportional to the battery discharge current. For example, on 30°C test, battery capacity at 2 Ohms, 3 Ohms and 4 Ohms respectively are 57.783, 58.74 and 60.467 Wh. Another example is on 2 Ohm load, battery capacity at 30°C, 40°C and 50°C are 57.783, 58.175 and 58.213 Wh respectively.

Accurate prediction of lithium-ion battery (LIB) capacity degradation is critical for reliable health management in applications such as electric vehicles and grid storage systems. Existing methods often fail to adequately model multi-scale temporal dependencies and exhibit training instability in deep neural architectures. To address these challenges, we propose a hierarchical multi-scale temporal network (HMSTN), featuring a novel multi-scale temporal block (MSTB). The MSTB integrates parallel convolutional branches with varying kernel sizes to capture localized fluctuations and incorporates a multi-head attention mechanism to model global cross-cycle degradation patterns. The hierarchical encoder–decoder architecture progressively downsamples input sequences by downsampling in the encoder to abstract long-term aging trends while restoring temporal resolution via skip connections and upsampling in the decoder to preserve critical short-term details. Auxiliary prediction heads at each encoder layer stabilize training through multi-task loss optimization, which effectively improves the overall loss function design. This mechanism establishes multi-path gradient flows, significantly improving robustness against training instability. Extensive experiments on different datasets demonstrate that HMSTN achieves superior accuracy in capacity prediction and exhibits strong generalization capabilities across diverse LIB chemistries and operating conditions.

Accurately estimating the capacity degradation of lithium-ion batteries (LIBs) is crucial for evaluating the status of battery health. However, existing data-driven battery state estimation methods suffer from fixed input structures, high dependence on data quality, and limitations in scenarios where only early charge–discharge cycle data are available. To address these challenges, we propose a capacity degradation estimation method that utilizes shorter charging segments for multiple battery types. A learning-based model called GateCNN-BiLSTM is developed. To improve the accuracy of the basic model in small-sample scenarios, we integrate a single-source domain feature transfer learning framework based on maximum mean difference (MMD) and a multi-source domain framework using the meta-learning MAML algorithm. We validate the proposed algorithm using various LIB cell and battery pack datasets. Comparing the results with other models, we find that the GateCNN-BiLSTM algorithm achieves the lowest root mean square error (RMSE) and mean absolute error (MAE) for cell charging capacity estimation, and can accurately estimate battery capacity degradation based on actual charging data from electric vehicles. Moreover, the proposed method exhibits low dependence on the size of the dataset, improving the accuracy of capacity degradation estimation for multi-type batteries with limited data.

This paper proposes a new model for state of charge estimation in Ni-Cd batteries, considering the various definitions of capacities and efficiencies that take place in the charging and discharging of the battery. First, the main variables used to determine the capacity of an electrochemical battery are described. Second, coulombic efficiency in charging and in discharging processes is studied. Then, the different capacities defined and efficiencies considered are mathematically related and included in the estimation model. With the new proposed model, the effect of temperature and current rate on the capacity of the battery is analysed. These two parameters are considered to be the most influencing parameters. Finally, a characterization test is carried out on a single 11 Ah Ni-Cd cell and the results are used to verify the performance of the proposed model.

A novel data-driven method for predicting the circulating capacity of lithium-ion battery under random variable current

The capacity allocation optimization of the energy storage system is an effective means to realize the absorption of renewable energy and support the safe and stable operation of a high proportion of new energy power systems. This paper constructs a microgrid structure including wind-power generation and hydrogen-electric hybrid energy storage. It proposes an optimization method for capacity allocation of the power grid system, which considers the battery capacity degradation. The method aims to improve the power economy, promote the consumption of new energy generation, and guarantee the stability and security of the power grid. It constructs the power grid capacity allocation optimization model with the power grid investment and operation cost, the battery capacity degradation, power supply stability, and green energy utilization as the objective functions. Experiments verified the effectiveness of the proposed method.